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\title{Fall Detection Research Report}   % type title between braces
\author{Guney Kayim}         % type author(s) between braces
\date{}

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This report is a summary for what we have researched lately over the 'Fall Detection' topic.

\section{Research}
\paragraph{}To gain insight about the topic several papers \cite{Anderson2006, Anderson2008, Rougier2011, Rougier2011a, Rougier2009} are read, and one of them \cite{Rougier2009} is selected to work on. We have picked that paper because it is intuitively more easy to understand and implement. Methods, features, and detection approach used on my study is written below. Results achieved are explained shortly.

\subsection{Methods}
\paragraph{}Here are the methods used in order the extract features from the image sequences. Why they are needed is explained.

\subsubsection{Background Estimation}
\paragraph{}Background estimation is used to extract people from the scene, since our focus is humans. Kalman filter based background estimator \cite{Scott} is used. It basically updates the background image by applying Kalman filter on each pixel. Results of this estimator is acceptable but it could be improved optimizing its parameters. Since it is not invariant to illumination differences and shadows (it is not in the implementation we used), some other background estimator(s) could be tried.

\subsubsection{Motion History Image}
\paragraph{}Motion History Image (MHI) is needed to select possible falls from the image sequence. Since MHI occurs when there is a motion, and brightness of the MHI differs depending on how big the motion is, it is very helpful. It is implemented as described in \cite{Bobick2001}.

\subsubsection{Ellipse Fitting}
\label{subsection_ellipse_fitting}
\paragraph{}Ellipse fitting is used to analyze the shape of humans. Ellipse is fitted on the foreground region extracted using background estimation. Ellipse parameters which we intend to use are the angle between the major axis of the ellipse and horizontal axis ($\theta$) and the ratio of the major axis and minor axis of the ellipse ($\rho$). These parameters are calculated using moments. \emph{There appears to be some problem in calculation of $\rho$ since it was not discriminative in experiments.}

\subsection{Features}
\paragraph{}The data retrieved from the methods are converted into features.

\subsubsection{Motion Quantity}
\paragraph{}Motion Quantity ($cMotion$) is a feature extracted using both MHI ($H_{\tau}$) and foreground region ($blob$). It is calculated as follows:
\begin{equation}
cMotion = \frac{\sum{_{Pixel(x,y)\in{blob}}H_{\tau}(x,y,t)}}{\#pixels\in{blob}}
\end{equation}
If there is a fast movement in the scene then there will be more MHI pixels in the foreground region and the cMotion value will be larger, or it will be low otherwise. So if $cMotion$ value is high then it can be said that there is a possible fall.

\subsubsection{Standard Deviation of $\theta$}
\paragraph{}There are several approaches to calculate $\sigma_\theta$. Here are some approaches.
\begin{enumerate}
\item Calculate the $\sigma_\theta$ using the $\theta$ values from the past 1 second, whenever a possible fall is detected. This approach is mentioned in \cite{Rougier2009}.
\item Take the $\theta$ values from consecutive possible fall frames and calculate $\sigma_\theta$ using them. This approach differs from the first one since this approach does not include any $\theta$ values other than the possible fall frames. This approaches is the one we used.
\end{enumerate}
\paragraph{}It could be discussed that which approach would result better. The motivation of using this feature is that if there is a large $cMotion$ caused by a walk event there won't be a large deviation in the values of $\theta$ so $\sigma_\theta$ will be low. On the other hand if large $cMotion$ is caused by a fall event then the value of $\theta$'s will change during the fall. This assumption is true if fall event is perpendicular to the cameras optical axis.

\subsubsection{Standard Deviation of $\rho$}
\paragraph{}The calculation of $\sigma_\rho$ is pretty much same with the $\sigma_\theta$. But as I mentioned in \ref{subsection_ellipse_fitting} there seems to be a problem in the calculation of $\rho$, so no experiments done based on this feature. But its motivation is to detect fall events parallel to the cameras optical axis.

\subsection{Detection Approach}

\subsubsection{Learning Based Detection}
\paragraph{}The first approach we tried is to train a classifier and detect falls using that classifier. The feature is 3 by 1 vector with the values $cMotion$, $\sigma_\theta$, and $\sigma_\rho$. When we were trying this approach we were not aware that $\rho$ values were miss calculated so it didn't perform well. Moreover, after we gave up on this approach, we have also changed the implementation of the $\theta$ calculation and tried optimize background estimator. Doe to these changes, after implementing and calculating $\rho$ values correctly this approach could be tried again. \emph{For this approach first calculation technique is used for both $\sigma_\theta$ and $\sigma_\rho$.}

\subsubsection{Thresholding Based Detection}
\paragraph{}After achieving unsuccessful results from the first approach we tend to use the approach mentioned at \cite{Rougier2009}. In this approach frames are eliminated step by step until only fall frames remain.
\begin{itemize}
\item Eliminate frames by checking $cMotion$ values. Use the ones left in next elimination step.
\item Eliminate frames by checking $\sigma_\theta$ values. Use the resulting ones as 'real fall candidate'.
\item Apply elimination on 'real fall candidates' by looking their fall duration and the time difference between the falls.
\end{itemize}
\paragraph{}After obtaining the results for all cameras, fall events are selected by majority voting from multiple camera results. \emph{For this approach second calculation technique is used for $\sigma_\theta$ and $\sigma_\rho$ is not used. It might be logical to apply this approach by using both $\sigma_\theta$ and $\sigma_\rho$. Also using first calculation technique could be another experiment to done. If first calculation is used, then majority voting can be applied for each frame. }

\subsection{Dataset}
\paragraph{}The dataset we used in this research has 192 videos in total from 8 cameras and 24 scenes. All of the data is annotated so it was rather simple to calculate the performance. Although the videos were not synchronized owner of the dataset delivered an offset matrix to synchronize the videos. Details of the dataset can be found at \cite{Rougier}.

\section{Conclusion}
\paragraph{}The research we have done about this topic was kind of satisfying but it was not enough. I'm sure after several reading and experiments the results will become more successful.

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